Authors
Atencio, D., Lee, H., and Manion, D.
Overview
Whether you are in the last hand of a Texas Hold’em game, asking a question in “Guess Who?”, deciding which card to play for your turn in Uno, or spinning the wheel for the game of Life, you are immersed in game strategies, probabilities, and chance. In this unit, students will explore the different concepts of probability and game theory behind a variety of popular games (i.e. Poker, Liar’s Dice, Mafia) while designing and creating their own game. The final artifact will be a prototype of an original game in the form of a board game, card game, or a similar form for at least 2 players. The game will include a printed rule book and a special “Insider’s Guide,” which will include the probability and math behind the game.
What is PBI?
Project Based Instruction (PBI) allows students to learn by applying new ideas. In short, PBI is characterized by 5 key elements: driving questions, situated inquiry, collaboration, learning technologies, and artifacts (Krajcik 2006). To be fully considered PBI, students must engage in activities that are important to them and similar to the actions adult professionals undertake which creates an atmosphere where new ideas are cultivated (Krajcik 2006). Also, PBI responds to education recommendations made by national organizations who “highlight the importance of students doing inquiry to promote personal decision making, participation in societal and cultural affairs, and economic productivity” (Krajcik 2006). Therefore, even when a unit includes the 5 key elements of PBI, the lessons must also engage the students in real, meaningful problems and build skills similar to that of a professional who participates actively in society to be considered PBI, otherwise, the unit will fall short of PBI standards.
When the unit can be defined as PBI, we see that Problem Based Instruction reflects current research about how people learn. With recent discoveries, we have learned that people learn based on four major ideas: (1) active constructions, (2) situated learning, (3) social interactions, and (4) cognitive tools (Krajcik 2006). PBI actively demonstrates how people learn through the 5 key elements.
Learning research has found that “deep understanding occurs when a learner actively constructs meaning based on his or her experiences and interaction in the world” (Krajcik 2006). The investigations and collaborations of PBI engage the students in active constructions to promote learning in the classroom. Also, learning is better situated in an authentic, real world context. In PBI, the driving questions and the development of artifacts resemble true scenarios a professional encounters in their responsibilities. From learning research, one of the most important findings is the role of social interaction in learning (Krajcik 2006). Individuals need to share, discuss, and refine ideas with others, and we can see PBI supports these needs by collaboration, investigations, and through the development of artifacts. Lastly, learning research has shown “cognitive tools can amplify and expand what students can learn” (Krajcik 2006). Through the use of learning technologies, PBI extends learning beyond normal lessons.
When the unit can be defined as PBI, we see that Problem Based Instruction reflects current research about how people learn. With recent discoveries, we have learned that people learn based on four major ideas: (1) active constructions, (2) situated learning, (3) social interactions, and (4) cognitive tools (Krajcik 2006). PBI actively demonstrates how people learn through the 5 key elements.
Learning research has found that “deep understanding occurs when a learner actively constructs meaning based on his or her experiences and interaction in the world” (Krajcik 2006). The investigations and collaborations of PBI engage the students in active constructions to promote learning in the classroom. Also, learning is better situated in an authentic, real world context. In PBI, the driving questions and the development of artifacts resemble true scenarios a professional encounters in their responsibilities. From learning research, one of the most important findings is the role of social interaction in learning (Krajcik 2006). Individuals need to share, discuss, and refine ideas with others, and we can see PBI supports these needs by collaboration, investigations, and through the development of artifacts. Lastly, learning research has shown “cognitive tools can amplify and expand what students can learn” (Krajcik 2006). Through the use of learning technologies, PBI extends learning beyond normal lessons.
5 Elements of PBI in this Unit
- Driving Question: How can we employ the use of probability and statistics to create a Family Game to present to the Hasbro?
- Situated Inquiry: The first 2 weeks of this unit are devoted to exploring different games by simply playing them. For example while students are playing Liar’s Dice, they will calculate the probability of a certain call at each turn. Additionally, students will explore game theory and optimal strategies via an inquiry into the Monty Hall problem, and analyze the relationship of area and probability.
- Collaboration: Students work in groups to create their game’s prototype, instruction manual and insider’s guide. Student groups peer review each other’s work at various milestones throughout the unit. Each group will also include a Group Contract.
- Learning Technologies: Students will use a spinner website simulation during the second day of the Spinner Investigation, and they will also use an interactive online poll system during the Deal or No Deal Benchmark and the Interactive Lecture. Depending on the type of test the students decide to analyze their games with, they may use technology such as Google Forms (for surveys) or Excel (for statistical analysis). Students will use word processing programs (such as Word) to write up their instruction manual and insider’s guide in an easily distributed digital form and they will also use a Powerpoint in their presentations.
- Artifacts: The artifact produced in this unit is a prototype game, with all necessary components represented in some form, along with a set of instructions, and an insider’s guide explaining the probability and statistics involved in the game.
Why is this Project Meaningful?
At times, there are some students who feel that math is very challenging and do not engage in the material or discussions due to a lack of confidence or connection with the lesson. Hence, our project was designed to showcase math in a light-hearted fashion where the challenges faced are similar to the problems that a professional game designer encounters in their field. Our project engages students with an entertaining style and demonstrates the use of probability and statistics in a profession where students could one day be an innovator. Additionally, our project incorporates critical reasoning where the students will need to evaluate real-life scenarios and develop strategies for an optimal decision.
Equitable Instruction
High Expectations and Opportunities
The equity principle states "equity requires high expectations and worthwhile opportunities for all" (Jamar 2005). The expectations for this unit are that students will take an active role in their own learning by participating, complete all assignments, and work maturely with a team. Since this is project-based instruction participation is not a question because collaboration is one of the key elements. All students must do their part in order for the team to be successful. The instructor will state these clearly on the first day and follow with a group contract in which the students will fill out their own expectations of group members. For the content, the detailed rubric of the final artifact will communicate the expectations of what the students need to know.
From our expectations, if students our proactive in their learning this experience will be worthwhile because they will develop more confidence in their ability in math. With our multiple investigation activities involving students playing games with each other in order to understand the math behind it, students will all have first-hand experiences with the probability concepts the unit is focused on. Creating high expectations is crucial in cultivating an equitable environment as this will empower students to learn (Jamar 2005), but there are still many practical needs for students.
Content Media
As this project involves a heavy use of additional resources to support instruction, such as videos, online software, and lecture slides, it is paramount that these tools are accessible and usable to all learners (Curry 2006). Therefore, the resources, referred to as content media, are designed to provide instruction that is accessible to a wide variety of students. The main evidence of our efforts is in this website created for the unit. The website was created on the basis of universal design which has a consistent layout, easy-to-read font, and easy navigation (Curry 2006). Accessibility is a higher priority than artistic, creative design. This will be a crucial resource for the students throughout the project as the calendar, all handouts, and the rubric will be available for download. Therefore, if a specific content or activity was confusing the student can go back to the website and redo at his or her own pace. In addition, since a website uses digital text “learners have multiple options for customizing the appearance and format of digital content” (Curry 2006). Students will be able to re-edit the documents in a way that works for them. Another resource the unit utilizes are videos. From the Poker launch event to lesson activities, videos assist in creating context for the content, providing another medium of communicating information, and entertainment, but if not fully aware videos could also hinder learning. Therefore, a universal design should be implemented in videos. Since there may be students with auditory disabilities the videos should be re-edited to include captions if the appropriate technology tools are available to the instructor (Curry 2006).
The equity principle states "equity requires high expectations and worthwhile opportunities for all" (Jamar 2005). The expectations for this unit are that students will take an active role in their own learning by participating, complete all assignments, and work maturely with a team. Since this is project-based instruction participation is not a question because collaboration is one of the key elements. All students must do their part in order for the team to be successful. The instructor will state these clearly on the first day and follow with a group contract in which the students will fill out their own expectations of group members. For the content, the detailed rubric of the final artifact will communicate the expectations of what the students need to know.
From our expectations, if students our proactive in their learning this experience will be worthwhile because they will develop more confidence in their ability in math. With our multiple investigation activities involving students playing games with each other in order to understand the math behind it, students will all have first-hand experiences with the probability concepts the unit is focused on. Creating high expectations is crucial in cultivating an equitable environment as this will empower students to learn (Jamar 2005), but there are still many practical needs for students.
Content Media
As this project involves a heavy use of additional resources to support instruction, such as videos, online software, and lecture slides, it is paramount that these tools are accessible and usable to all learners (Curry 2006). Therefore, the resources, referred to as content media, are designed to provide instruction that is accessible to a wide variety of students. The main evidence of our efforts is in this website created for the unit. The website was created on the basis of universal design which has a consistent layout, easy-to-read font, and easy navigation (Curry 2006). Accessibility is a higher priority than artistic, creative design. This will be a crucial resource for the students throughout the project as the calendar, all handouts, and the rubric will be available for download. Therefore, if a specific content or activity was confusing the student can go back to the website and redo at his or her own pace. In addition, since a website uses digital text “learners have multiple options for customizing the appearance and format of digital content” (Curry 2006). Students will be able to re-edit the documents in a way that works for them. Another resource the unit utilizes are videos. From the Poker launch event to lesson activities, videos assist in creating context for the content, providing another medium of communicating information, and entertainment, but if not fully aware videos could also hinder learning. Therefore, a universal design should be implemented in videos. Since there may be students with auditory disabilities the videos should be re-edited to include captions if the appropriate technology tools are available to the instructor (Curry 2006).
Special Accomodations
For those whose native language is not English following along the class curriculum is difficult. Not only is understanding English already a struggle, but the way English Language Learners (ELLs) view math may be different if not from a Western society (Edmonds 2009). The following are practical ways to assist ELLs in following along with the material, but are also beneficial to other students as well such as those who struggle with reading or students with dyslexia. Since “ELLs are often placed in mainstream [math] classes long before they are fluent in English” (Reville 2006) students may get lost during a lecture. Therefore our activities are designed with ‘markers,’ which are points during a lesson to help students get back on track if they get lost, and multiple representations such as visuals (Edmonds 2009). The instructor is intentional in ‘checking in’ on students to make sure everyone is on the same page. The instructor will also establish a culture of healthy participation during discussion. For some students, speaking up is difficult while other students may dominate a conversation. Therefore, at the beginning of the unit the instructor will remind students of the idea of ‘taking on the floor’ and ‘giving the floor,’ which emphasizes a balance between speaking up and listening (Edmonds 2009). This will encourage everyone to participate. In addition, all formal assignments have a good and bad example so that students know what the instructor is expecting (Edmonds 2009). For students with learning disabilities the instructor will collaborate with the special education teacher to plan appropriate strategies and to know how to implement different parts of the lesson based on students’ individual needs (Steele 2008).
References
Curry, C. Cohen, L, Lightbody, N. (2006). Universal Design in Science Learning. The Science Teacher (pp. 33-34).
Jamar, Idorenyin, & Pitts, Vanessa R. (2005). High Expectations: A 'How' of Achieving Equitable Mathematics Classroom.
Krajcik, J. S., & Blumenfeld, P. C. (2006). Project-Based Learning. In R. K. Sawyer (Ed.), The Cambridge handbook of the Learning Sciences (pp. 317-333). New York: Cambridge Press
Reville, P. (2006). Implementing policy for English language learners. Rennie Center for Education and Research. www. renniecenter.org/junie-e-forum-web.html
Steele, Marcee M. (2008). Helping Students with Learning Disabilities. The Science Teacher (pp. 38-42).
Jamar, Idorenyin, & Pitts, Vanessa R. (2005). High Expectations: A 'How' of Achieving Equitable Mathematics Classroom.
Krajcik, J. S., & Blumenfeld, P. C. (2006). Project-Based Learning. In R. K. Sawyer (Ed.), The Cambridge handbook of the Learning Sciences (pp. 317-333). New York: Cambridge Press
Reville, P. (2006). Implementing policy for English language learners. Rennie Center for Education and Research. www. renniecenter.org/junie-e-forum-web.html
Steele, Marcee M. (2008). Helping Students with Learning Disabilities. The Science Teacher (pp. 38-42).